5.12
Some hypothetical alloy is composed of 25 wt% of metal A and 75 wt% of metal B.
If the
densities of metals A and B are 6.17 and 8.00 g/cm
3
, respectively, whereas their respective atomic weights
are 171.3 and 162.0 g/mol, determine whether the crystal structure for this alloy is simple cubic, face
centered cubic, or bodycentered cubic.
Assume a unit cell edge length of 0.332 nm.
Solution
In order to solve this problem it is necessary to employ Equation 3.5;
in this expression density
and atomic weight will be averages for the alloy—that is
ρ
ave
=
nA
ave
V
C
N
A
Inasmuch as for each of the possible crystal structures, the unit cell is cubic, then
V
C
=
a
3
, or
ρ
ave
=
nA
ave
a
3
N
A
And, in order to determine the crystal structure it is necessary to solve for
n
, the number of atoms
per unit cell.
For
n
=1, the crystal structure is simple cubic, whereas for
n
values of 2 and 4, the crystal
structure will be either BCC or FCC, respectively. When we solve the above expression for
n
the result is
as follows:
n
=
ρ
ave
a
3
N
A
A
ave
Expressions for
A
ave
and
ρ
ave
are found in Equations 5.14a and 5.13a, respectively, which, when
incorporated into the above expression yields
n
=
100
C
A
ρ
A
+
C
B
ρ
B
a
3
N
A
100
C
A
A
A
+
C
B
A
B
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentSubstitution of the concentration values (i.e.,
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 shang
 Diamond cubic, AAVE, Crystal system, Chemical Properties, Atomic packing factor

Click to edit the document details